"The Chaser" employs what's called situational irony. This is a situation where actions have an effect that is the exact opposite of what was intended. Alan wants to buy a love potion but will almost certainly end up returning to buy poison to kill his future wife when he gets tired of her constant, unwavering attention.

Another example of irony comes in the huge disparity in cost between the love potion and the poison, the "chaser" of the title. One would think that love would be much more precious, more valuable. And yet the love potion costs only a dollar, whereas the poison will set Alan back a cool five thousand dollars.

Then we have an example of verbal irony. When the old man says "Please a customer with one article, and he will come back when he needs another," he sounds ever so kindly and helpful. Yet in actual fact he's subtly hinting at the sinister nature of his business.

Finally, there's dramatic irony, where we know something one of the characters doesn't. We sense that when the old man tells Alan how his future wife "will never allow you to tire, to sit in a draught, to neglect your food" that this is something that he'll soon grow weary of. Hence the old man is able to assert, with complete confidence, that his customers will always come back to buy some "life-cleaner."

The irony in “The Chaser” is that the young man comes looking for a love potion, but will be looking for a death potion later.

Irony is when something unexpected happens.  In this story, the title is ironic.  At the end of the story, the old man says, "Au revoir," which means he thinks he will be seeing Alan again.

At the end of the story, the old man implies that he sells the love potion for one dollar because people buy it when they are young and naïve, but later in life they will buy the potion that kills the person they once wanted to fall in love with them, for five thousand dollars.

"I like to oblige," said the old man. "Then customers come back, later in life, when they are better off, and want more expensive things. Here you are. You will find it very effective."  (p. 3)

A chaser is “a drink drunk after another of a different kind” (freedictionary.com).  The title of the story is ironic because it implies that the young man is going to return for the chaser eventually.  He will get the woman to fall in love with him, but someday he will not be able to stand it and he will come back to get the potion to kill her.